Phenomenology of the 1/N$_f$ Expansion for Field Theories in Extra Dimensions

TL;DR

This paper reviews the 1/N_f expansion in multidimensional field theories, highlighting its renormalizability, the role of ghost states, and applications to scattering processes and gauge coupling unification.

Contribution

It introduces the properties of the 1/N_f expansion in extra-dimensional theories, emphasizing its renormalizability and physical implications, including unitarity conditions.

Findings

The 1/N_f expansion is renormalizable with only logarithmic divergences.

Ghost states may not affect physical amplitudes, preserving unitarity.

Gauge coupling unification occurs at lower energies in multidimensional models.

Abstract

In this paper we review the properties of the 1/$N_f$ expansion in multidimensional theories. Contrary to the usual perturbative expansion it is renormalizable and contains only logarithmic divergencies. The price for it is the presence of ghost states which, however, in certain cases do not contribute to physical amplitudes. In this case the theory is unitary and one can calculate the cross-sections. As an example we consider the differential cross section of elastic $eq \to eq$ scattering in $D=7,11,...$-dimensional world. We look also for the unification of the gauge couplings in multidimensional Standard Model and its SUSY extension which takes place at energies lower than in 4 dimensions.